The France international has spent the last five years in the Spanish capital and his performances have received such acclaim that he has twice come third in the Ballon d'Or voting.
The 28-year-old has been Atletico's main source of goals once again this term, netting 21 in over 40 appearances across all competitions.
Barcelona has been touted as a possible next destination for Greizmann, despite the fact he signed a fresh deal at Wanda Metropolitano only last year, but Koke is hoping he stays put for the long term.
"The player has shown what he is at Atletico," Koke told Marca.
"We want him to continue, to be motivated, to continue to make history. Hopefully the day he leaves us will be a goodbye like Godin's."
Godin is leaving Atletico after nine years and Koke was keen to pay tribute to his departing team-mate, who has won La Liga, the Copa del Rey and two Europa Leagues with the club, while also reaching two Champions League finals.
"How could you not be emotional? I've gone through a lot with him," Koke added.
"He's been one of the leaders of one of the best eras. We want the best for him."
Diego Simeone's side are destined to finish the 2018-19 campaign without silverware, with a runners-up spot behind champions Barcelona already confirmed.